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Simulating magnetic positive positioning of cryogenic propellants in a transient acceleration field
Abstract
A computational simulation of magnetic positive positioning (MP2) is developed to model cryogenic propellant reorientation in reduced gravity. Previous efforts have successfully incorporated an electromagnetic field model into an axisymmetric, two-dimensional, incompressible fluid flow model yielding accurate predictions of fluid motion induced by a magnetic field. To simulate MP2, a three-dimensional magnetic field and magnetic force model was developed as a feature of a commercially available fluid flow model which has been well validated. The computational tool was then improved upon to model magnetically induced flows in a transient acceleration field. Simulation predictions obtained with the enhanced model are compared to available reduced gravity experiment data. Evidence is presented and conclusions are drawn that support the continued use of the simulation as viable modeling and predictive tool in the continuing study of MP2.
... Temporal discretization is accomplished using implicit time integration, which is unconditionally stable with respect to time step size. Solutions are subsequently iterated at each time level until the convergence criteria are met (Marchetta and Roos 2009). The geometric reconstruction scheme is used to reconstruct the interface between fluids using a piecewiselinear approach. ...
The computational and experimental studies have been performed to investigate the hydrodynamic process of liquid propellant reorientation for the launch vehicle series fuel tanks in microgravity environment. The VOF method was used to simulate the free surface flow of gas-liquid. The process of the liquid propellant reorientation started from initially curved interface at low Bond number. The propellant reorientation flow procedure at high Bond number was obtained from numerical simulation and scale model experiment in drop tower. The numerical results agreed well with the experiments. The results can be used to adjust the engineering reorientation parameters.
... There have been some small experiments such as MAPO 16 , which have been flown on the NASA zero-gravity airplane (Vomit Comet). Coupled fluid/electromagnetic models were correlated to the experimental results 17,18,19 . Analytical work has begun this year using those models to determine the feasibility of using magnetic propellant positioning for tanks on the scale required for propellant depots. ...
Orbital cryogenic propellant depots and the ability to refuel spacecraft in orbit are critical capabilities for the expansion of human life throughout the Solar System. While depots have long been recognized as an important component of large-scale manned spaceflight efforts, questions about their technology readiness have so far prevented their implementation. Technological advancements in settled cryogenic handling, passive thermal control systems, and autonomous rendezvous and docking techniques make near-term implementation of cryogenic propellant depots significantly more realistic. Current work on flight-demonstration tools like ULA's CRYOTE testbed, and Masten Space Systems's XA-1.0 suborbital RLV provide methods for affordably retiring the remaining technical risks for cryogenic depots. Recent depot design concepts, built on high-TRL technologies and existing flight vehicle hardware, can enable easier implementation of first-generation propellant depots without requiring extensive development programs. Some concepts proposed by industry include disposable "pre-depots", single-fluid simple depots, self-deployable dual-fluid single-launch depots using existing launchers and near-term launcher upgrades, and multi-launch modular depots. These concepts, particularly the dual-fluid single-launch depot enable robust exploration and commercial transportation throughout the inner Solar System, without the need for HLVs, while providing badly-needed markets to encourage the commercial development of more affordable access to space.
A computational model is described and implemented in this work to analyze the performance of a ferrofluid based electromagnetic energy harvester. The energy harvester converts ambient vibratory energy into an electromotive force through a sloshing motion of a ferrofluid. The computational model solves the coupled Maxwell’s equations and Navier-Stokes equations for the dynamic behavior of the magnetic field and fluid motion. The model is validated against experimental results for eight different configurations of the system. The validated model is then employed to study the underlying mechanisms that determine the electromotive force of the energy harvester. Furthermore, computational analysis is performed to test the effect of several modeling aspects, such as three-dimensional effect, surface tension, and type of the ferrofluid-magnetic field coupling on the accuracy of the model prediction.
We present the RIPPLE computer program* for modeling transient, two-dimensional, incompressible fluid flows with surface tension on free surfaces of general topology. Finite difference solutions to the incompressible Navier-Stokes equations are obtained on an Eulerian, rectilinear mesh in Cartesian or cylindrical geometries. Free surfaces are represented with volume-of-fluid (VOF) data on the mesh. Surface tension is modeled as a volume force derived from the continuum surface force ( CSF) model. A two-step projection method is used for the incompressible fluid flow solutions, aided by an incomplete Cholesky conjugate gradient (ICCG) solution technique for the pressure Poisson equation (PPE). Momentum advection is estimated with the weakly monotonic, second order upwind method of van Leer. Flow obstacles and curved boundaries interior to the mesh are represented with a partial cell treatment. The improvements and enhancements of RIPPLE relative to its predecessor, NASA-VOF2D, have resulted in a versatile tool capable of modeling a wide range of applications, being especially suited for low-Bond number, low-Weber number, and low-Capillary number flows in which fluid accelerations are weak and fluid restoring forces (e.g., surface tensions) are strong. After a brief summary of the primary features of RIPPLE, we describe the model equations, the numerical method, and the structure of the computer program. Example calculations then illustrate the method's properties, with instructions given on the use of the program.
The impulsive propellant reorientation process is modeled using the Energy Calculations for Liquid Propellants in a Space Environment (ECLIPSE) code. A brief description of the process and the computational model is presented. Code validation is documented via comparison to experimentally derived data for small scale tanks. Predictions of reorientation performance are presented for two tanks designed for use in flight experiments and for a proposed full scale OTV tank. A new dimensionless parameter is developed to correlate reorientation performance in geometrically similar tanks. Its success is demonstrated.
Optimization of the propellant reorientation process can provide increased payload capability and extend the service life of spacecraft. The use of pulsed propellant reorientation to optimize the reorientation process is proposed. The ECLIPSE code was validated for modeling the reorientation process and is used to study pulsed reorientation in small-scale and full-scale propellant tanks. A dimensional analysis of the process is performed and the resulting dimensionless groups are used to present and correlate the computational predictions for reorientation performance.
A phenomenological treatment is given for the fluid dynamics and thermodynamics of strongly polarizable magnetic fluid continua in the presence of nonuniform magnetic fields. Examples of the fluids treated here have only recently been synthesized in the laboratory. It is found that vorticity may be generated by thermomagnetic interaction even in the absence of viscosity and this leads to the development of augmented Bernoulli relationships. An illustration of a free-surface problem of static equilibrium is confirmed by experiment and information is obtained regarding a fluid's magnetic susceptibility. Another illustration elucidates the mechanism of an energy conversion technique. Finally, an analytical solution is found for the problem of source flow with heat addition in order to display the thermomagnetic and magnetomechanical effects attendant to simultaneous heat addition and fluid motion in the presence of a magnetic field.
A series of experiments have been performed investigating the use of magnets to orient fluids in a lowgravity environment. The fluid of interest for this project was liquid oxygen (LO2) since it exhibits a paramagnetic behavior (is attracted to magnetic fields). However, due to safety and handling concerns, a water-based ferromagnetic mixture (produced by Ferrofluidics Corporation) was selected to simplify procedures. Three ferromagnetic fluid mixture strengths and a nonmagnetic water baseline were tested using three different initial fluid positions with respect to the magnet. Experiment accelerometer data were used with a modified computational fluid dynamics code (CFD) termed CFX-4 (by AEA Technologies) to predict fluid motion. These predictions compared favorably with experiment video data, verifying the code's ability to predict fluid motion with and without magnetic influences. Additional predictions were generated for LO2 with the same conditions and geometries used in the flight-testing. Test hardware consisted of a cylindrical Plexiglas tank (6-in. bore with 10-in. length), a 6,000-Gauss rare Earth ringmagnet, three-axis accelerometer package, computer, and a video recorder system. All tests were conducted aboard the NASA Reduced-Gravity Workshop, a KC-135 aircraft.
BACKGROUND For more than 30 years, analytical 1 , experimental 2 , and computational 3 studies have been performed to seek reliable technologies for managing cryogenic propellants in reduced gravity. Passive and impulsive systems have been utilized for monopropellant management onboard small satellites. Passive systems depend on surface tension forces generated by specific geometries, such as screens, vanes, and channels, inside the tank, to hold the propellant within specific locations inside the tank 4,5 . One disadvantage of the passive system is the increased weight of the spacecraft due to the vane/screen/channel structures. Active systems achieve reorientation by firing external thrusters that accelerate the spacecraft tank relative to the liquid 3,6 . The advantage propulsive methods have over passive systems is that propellant can be repositioned to meet mission requirements. However, implementation requires the addition of auxiliary thrusters, fuels, and controls. Experimental and computational studies have shown that a sufficiently strong magnetic field can influence a magnetically susceptible liquid. An improved simulation integrates an electromagnetic field model and incompressible flow model to predict fluid reorientation using realistic magnetic fields. Flow fields are presented incorporating several realistic magnetic fields to verify and validate the connectivity of the integrated system. Conclusions are drawn about the fidelity of the integrated simulation in modeling magnetically induced fluid flows. The simulation is used to model the application of magnetic positive positioning of LOX in a reduced gravity experiment utilizing a realistic magnetic field. Preflight experiment predictions of the performance of the magnetic field in reorienting LOX are presented and recommendations are made for future design.
A computational simulation is used to model magnetically induced cryogenic propellant flows in reduced gravity. Simulations of magnetic positive positioning and storage of LOX are presented and evaluated. The influence of the magnetic field and its feasibility for use in each respective application is explored. The magnetic Bond number is utilized as predictive correlating parameter for investigating these processes. Evidence is presented to support the hypothesis that magnetic fields may be an attractive option for positive positioning of cryogenic propellants in future spacecraft systems and the hypothesis that the magnetic Bond number is an effective dimensionless parameter for modeling and understanding such systems. © 2002 by J. G. Marchetta, J. I. Hochstein, D. R. Sauter, and B. D. Simmons.
A computational simulation is used to model magnetically induced LOX flows in reduced gravity. Simulations of magnetic positive positioning of LOX are presented and the influence of the magnetic field and background acceleration on reorientation timing is explored. A dimensionless reorientation time is sought to compliment the magnetic Bond number and Bond number as an additional predictive correlating parameter for scaling this process. Evidence is presented to support the hypothesis that magnetic fields may be an attractive option for positive positioning of cryogenic propellants in future spacecraft systems and the hypothesis that these correlating parameters are an effective means for modeling and understanding such systems.
This book presents fundamental material on the structure and properties
of magnetic fluids (MFs). The topics discussed include: thermomechanic
equations for MFs of equilibrium magnetization, statics of MFs,
thermoconvective phenomena, surface phenomena, equations of
thermomechanics of MFs with relaxing magnetization in low-frequency
approximation, main effects of volume magnetic couples in a uniform
field, the effect of transverse stresses on the structure of
two-dimensional flows in a uniform field, and dynamic interaction
between MFs and a nonuniform field.
The free surface behaviour of a volatile wetting liquid at low gravity is studied using scaling and numerical techniques. An open cavity model, which was applied in part 1 to investigate fluid flow and heat transfer in non-deforming pores, is used to evaluate the influence of convection on surface morphology with length scales and subcooling/superheating limits of 1 [less-than-or-equal] D [less-than-or-equal] 102 μm and [similar] 1 K, respectively. Results show that the menisci shapes of highly wetting fluids are sensitive to thermocapillary flow and to a lesser extent the recoil force associated with evaporation and condensation. With subcooling, thermocapillarity produces a suction about the pore centreline that promotes loss of mechanical equilibrium, while condensation exerts an opposing force that under some conditions offsets this destabilizing influence. With superheating, thermocapillarity and evaporation act in the same direction and mutually foster surface stability. All of these trends are magnified by high capillary and Biot numbers, and the stronger circulation intensities associated with small contact angles. These phenomena strongly depend on the thermal and interfacial equilibrium between the liquid and vapour, and have important ramifications for systems designed to maintain a pressure differential across a porous surface.
Axisymmetric shapes and stability of nonlinearly polarizable dielectric (ferrofluid) drops of fixed volume which are pendant/sessile on one plate of a parallel-plate capacitor and are subjected to an applied electric (magnetic) field are determined by solving simultaneously the free boundary problem comprised of the Young-Laplace equation for drop shape and the Maxwell equations for electric (magnetic) field distribution. Motivated by the desire to explain certain experiments with ferrofluids, a constitutive relation often used to describe the variation of polarization with applied field strength is adopted here to close the set of equations that govern the distribution of electric field. Specifically, the nonlinear polarization, P, is described by a Langevin equation of the form P = α[coth (τE) −1/(τE)], where E is the electric field strength. As expected, the results show that nonlinearly polarizable drops behave similarly to linearly polarizable drops at low field strengths when drop deformations are small. However, it is demonstrated that at higher values of the field strength when drop deformations are substantial, nonlinearly polarizable supported drops whose contact lines are fixed, as well as ones whose contact angles are prescribed, display hysteresis in drop deformation over a wide range of values of the Langevin parameters α and τ. Indeed, properly accounting for the nonlinearity of the polarization improves the quantitative agreement between theory and the experiments of Bacri et
al. (1982) and Bacri & Salin (1982, 1983). Detailed examination of the electric fields inside nonlinearly polarizable supported drops reveals that they are very non-uniform, in contrast to the nearly uniform fields usually found inside linearly polarizable drops.
The problem of steady motion and thermal behaviour of a volatile, wetting liquid in an open cavity under low gravity is defined and examined. The domain geometrically approximates a two-phase pore of liquid on a wicking structure surface, and consists of a 1 to 102 μu wide rectangular cavity bounded by a saturated vapour and liquid reservoir on its upper and lower surfaces, respectively. Thermal non-equilibrium and convection are established by symmetrically superheating or subcooling the pore boundaries by [similar] 1 K relative to the vapour. Numerical analyses show that although thermocapillary flow competes with interfacial phase change in dictating the circulation and flow structure, it tends to reinforce the convective effects of evaporation and condensation on surface temperature and heat transport. In addition, highly wetting fluids with curved menisci are characterized by greater circulation intensities and dynamic pressure gradients than a flat surface. The magnitude of these gradients suggests that the fixed menisci shapes assumed in this study are unrealistic, and that the influence of convection on surface morphology should be considered.
A set of hydrodynamic equations has been applied to processes occurring in non-conductive fluids placed into magnetic fields. The equations are valid for equilibrium magnetization within the framework of a continuous medium. The ranges of physical parameters have been evaluated for which magnetization of a fluid should be taken into account in problems concerning the determination of equilibrium forms, and flows and their stability. The conclusion has been drawn that magnetization of natural fluids in these problems must be taken into consideration for fluids in high (exceeding 1 T) magnetic fields. As examples, the solutions of several typical problems concerning the equilibrium surface of capillary fluids and their stability in external magnetic fields have been considered. Hydrodynamic effects related to magnetization of natural capillary fluids in high magnetic fields are studied with due regard for the above solutions. Hydrodynamic effects in para- and diamagnetic fluids have been studied and the common and distinctive features of these effects discussed.
A phenomenological treatment is given for the fluid dynamics and thermodynamics of strongly polarizable magnetic fluid continua in the presence of nonuniform magnetic fields. Examples of the fluids treated here have only recently been synthesized in the laboratory. It is found that vorticity may be generated by thermomagnetic interaction even in the absence of viscosity and this leads to the development of augmented Bernoulli relationships. An illustration of a free‐surface problem of static equilibrium is confirmed by experiment and information is obtained regarding a fluid's magnetic susceptibility. Another illustration elucidates the mechanism of an energy conversion technique. Finally, an analytical solution is found for the problem of source flow with heat addition in order to display the thermomagnetic and magnetomechanical effects attendant to simultaneous heat addition and fluid motion in the presence of a magnetic field.
An existing empirical analysis relating to the reorientation of liquids in cylindrical tanks due to propulsive settling in a low gravity environment was extended to include the effects of geyser formation in the Weber number range from 4 to 10. Estimates of the minimum velocity increment required to be imposed on the propellant tank to achieve liquid reorientation were made. The resulting Bond numbers, based on tank radius, were found to be in the range from 3 to 5, depending upon the initial liquid fill level, with higher Bond number required for high initial fill levels. The resulting Weber numbers, based on tank radius and the velocity of the liquid leading edge, were calculated to be in the range from 6.5 to 8.5 for cylindrical tanks having a fineness ratio of 2.0, with Weber numbers of somewhat greater values for longer cylindrical tanks. It, therefore, appeared to be advantageous to allow small geysers to form and then dissipate into the surface of the collected liquid in order to achieve the minimum velocity increment. The Bond numbers which defined the separation between regions in which geyser formation did and did not occur due to propulsive settling in a spherical tank configuration ranged from 2 to 9 depending upon the liquid fill level.
An experimental program was conducted to examine the liquid flow patterns that result from the axial jet mixing of ethanol in 10-centimeter-diameter cylindrical tanks in weightlessness. A convex hemispherically ended tank and two Centaur liquid-hydrogen-tank models were used for the study. Four distinct liquid flow patterns were observed to be a function of the tank geometry, the liquid-jet velocity, the volume of liquid in the tank, and the location of the tube from which the liquid jet exited.
This report details the results of a series of fluid motion experiments to investigate the use of magnets to orient fluids in a low-gravity environment. The fluid of interest for this project was liquid oxygen (LO2) since it exhibits a paramagnetic behavior (is attracted to magnetic fields). However, due to safety and handling concerns, a water-based ferromagnetic mixture (produced by Ferrofluidics Corporation) was selected to simplify procedures. Three ferromagnetic fluid mixture strengths and a nonmagnetic water baseline were tested using three different initial fluid positions with respect to the magnet. Experiment accelerometer data were used with a modified computational fluid dynamics code termed CFX-4 (by AEA Technologies) to predict fluid motion. These predictions compared favorably with experiment video data, verifying the code's ability to predict fluid motion with and without magnetic influences. Additional predictions were generated for LO2 with the same test conditions and geometries used in the testing. Test hardware consisted of a cylindrical Plexiglas tank (6-in. bore with 10-in. length), a 6,000-G rare Earth magnet (10-in. ring), three-axis accelerometer package, and a video recorder system. All tests were conducted aboard the NASA Reduced-Gravity Workshop, a KC-135A aircraft.
The non-linear magnetization characteristics of recently developed ferrofluids complicate studies of wave dynamics and stability. A general formulation of the incompressible ferrohydrodynamics of a ferrofluid with non-linear magnetization characteristics is presented, which distinguishes clearly between effects of inhomogeneities in the fluid properties and saturation effects from non-uniform fields. The formulation makes it clear that, with uniform and non-uniform fields, the magnetic coupling with homogeneous fluids is confined to interfaces; hence, it is a convenient representation for surface interactions.
Detailed attention is given to waves and instabilities on a planar interface between ferrofluids stressed by an arbitrarily directed magnetic field. The close connexion with related work in electrohydrodynamics is cited, and the effect of the non-linear magnetization characteristics on oscillation frequencies and conditions for instability is emphasized. The effects of non-uniform fields are investigated using quasi-one-dimensional models for the imposed fields in which either a perpendicular or a tangential imposed field varies in a direction perpendicular to the interface. Three experiments are reported which support the theoretical models and emphasize the interfacial dynamics as well as the stabilizing effects of a tangential magnetic field. The resonance frequencies of ferrohydrodynamic surface waves are measured as a function of magnetization, with fields imposed first perpendicular, and second tangential, to the unperturbed interface. In a third experiment the second configuration is augmented by a gradient in the imposed magnetic field to demonstrate the stabilization of a ferrofluid surface supported against gravity over air; the ferromagnetic stabilization of a Rayleigh-Taylor instability.
The use of pulsed thrust to optimize the propellant reorientation process is proposed. The ECLIPSE code is used to study the performance of pulsed reorientation in small-scale and full-scale propellant tanks. A dimensional analysis of the process is performed and the resulting dimensionless groups are used to present and correlate the computational predictions of reorientation performance. Based on the results obtained from this study, it is concluded that pulsed thrust reorientation seems to be a feasible technique for optimizing the propellant reorientation process across a wide range of spacecraft, for a variety of missions, for the entire duration of a mission, and with a minimum of hardware design and qualification.
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